We present a multiloop flow equation for the four-point vertex in the functional renormalization group (fRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order. This provides substantial improvement of fRG computations for the four-point vertex and, consequently, the self-energy. Using the X-ray-edge singularity as an example, we show that solving the multiloop fRG flow is equivalent to solving the (first-order) parquet equations and illustrate this with numerical results.
@article{arxiv.1703.06505,
title = {Multiloop functional renormalization group that sums up all parquet diagrams},
author = {Fabian B. Kugler and Jan von Delft},
journal= {arXiv preprint arXiv:1703.06505},
year = {2018}
}